Topology & Geometric Group Theory Seminar

Fall 2007

1:30 - 2:30, Malott 253

Tuesday, October 30

Yvonne Lai, UC Davis

Using simplicial trees to generate an effective compactness theorem for Coxeter groups

Through highly non-constructive methods, works by Bestvina, Culler, Morgan, Paulin, Rips, Shalen, and Thurston show that if a finitely presented group does not split over a small subgroup, then the space of its discrete and faithful actions on Hn, modulo conjugation, is compact for all dimensions. We make this result effective for Coxeter groups. By fixing a presentation and associating a simplicial tree to a given action, we find that either the group splits over a small subgroup or there is a constant C and a point in Hn that is moved no more than C by any generator. The constant C depends only on n and the number of generators in the presentation.

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